Introduction to Several Concepts of Convexity and Semicontinuity for Function from $\Bbb R$ to $\Bbb R$

Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Introduction to Several Concepts of Convexity and Semicontinuity for Function from $\Bbb R$ to $\Bbb R$

Noboru Endou: Shinshu University, Nagano
Katsumi Wasaki: Shinshu University, Nagano
Yasunari Shidama: Shinshu University, Nagano

Summary.

This article is an introduction to convex analysis. In the beginning, we have defined the concept of strictly convexity and proved some basic properties between convexity and strictly convexity. Moreover, we have defined concepts of other convexity and semicontinuity, and proved their basic properties.

MML Identifier: RFUNCT_4

The terminology and notation used in this paper have been introduced in the following articles [16] [18] [1] [19] [5] [2] [10] [13] [8] [17] [6] [7] [11] [9] [15] [12] [3] [4] [14]

Contents (PDF format)

Some Useful Properties of $n$-Tuples on ${\Bbb R}$
Convex and Strictly Convex Functions
Definitions of Several Convexity and Semicontinuity Concepts

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Received March 23, 2000

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